Analysis of factors influencing surface settlement during shield construction of a double-line tunnel in a mudstone area

Urban rail transit is widely used in major cities worldwide due to its high efficiency, safety, and environmental friendliness. Shield construction has a fast excavation speed and a negligible impact on ground transportation; thus, it is the preferred construction method for urban rail transit tunnels. Mudstone is a widely distributed soft rock characterized by large deformation, low strength, and significant rheological differences in different areas. Mudstone causes problems in the design and construction of subways. This paper uses finite element analysis to establish a three-dimensional numerical model of a double-line tunnel in a weathered mudstone area and analyze the influence of the stratum, design, and construction parameters on surface settlement and deformation during asynchronous and simultaneous shield construction. The research results show that the lateral surface settlement curve obtained from the simulation is consistent with the measured data, demonstrating the reliability and feasibility of the three-dimensional numerical model. The surface settlement is affected by the deformation modulus, cohesion, and the angle of internal friction, and the deformation modulus has the most significant impact. The surface settlement decreases as the buried depth of the tunnel or the distance between the two center lines of the two tunnels increases. As the buried depth of the double-lane tunnel decreases or the distance between the two center lines of the two tunnels increases to a certain value, the lateral surface settlement curve exhibits two peaks. The surface settlement shows a decreasing trend with an increase in the thrust of the shield machine and an improvement in the grouting quality. However, excess grouting pressure causes surface uplift and a subsequent increase in surface subsidence.

Shield construction has a fast excavation speed and a relatively small impact on ground transportation. It has become the preferred construction method for urban rail transit tunnels and urban subway construction 1 . Surface settlement caused by shield construction and the resulting damage to adjacent buildings are important problems during subway construction, especially in certain types of strata 2 . Mudstone is a widely distributed soft rock prone to large deformation, has low strength, and exhibits significant rheological differences in different areas. Weathered mudstone disintegrates rapidly when it loses water and softens when it comes into contact with water. These characteristics result in challenges for shield tunneling in mudstone formations 3,4 .
The influence of different parameters on the surface settlement during shield construction of double-line tunnels in mudstone areas is unclear, complicating the prediction and control of surface settlement. Peck's equation is commonly used to analyze surface settlement during shield construction 5 . Suwansawat et al. 6 analyzed surface settlement data of double-line shield construction in a clay layer in Bangkok and found that an empirical equation could be used to estimate surface settlement during the construction of a double-line tunnel or doubleline superimposed tunnel. The tunneling pressure, grouting pressure, and other shield construction parameters significantly affected the settlement range and maximum settlement. Zheng 7 used an empirical equation to analyze surface settlement caused by the tunnel construction of the Changchun Metro Line 1 through clay and mudstone layers. The result showed a good agreement between the measured data and theoretical calculations. The authors proposed a correction coefficient for the empirical equation suitable for the study area. However, empirical equations are typically only applicable to specific locations, require sufficient and accurate measurement www.nature.com/scientificreports/   www.nature.com/scientificreports/ at cross-sections every 50 m within the 100 m range of the shield starting and hoisting section, and monitoring cross-sections were located every 100 m in the remaining sections. The cross-section monitoring points were located at the centers of the left and right tunnels, with a spacing of 3~5 m. The layout of the settlement monitoring points of the shield tunnel is shown in Figs. 3 and 4. We calculated the settlement amount, deformation rate, cumulative settlement, and other data in each construction stage using the elevation data at the monitoring points. After the excavation of the double tunnel was completed, the settlement of DB-1, DB-2, and DB-3 in the transverse monitoring sections was measured. The surface settlement curve is shown in Fig. 5.
The three surface settlement curves conform to Peck's equation 5 . The tunnel's burial depth is the shallowest in the DB-1 monitoring section, and the surface settlement is larger due to construction mode conversion. The burial depth is the deepest and the surface settlement is the smallest in the DB-3 monitoring section. The monitoring results provide information on the surrounding environment, the support structure, and the soil dynamics during construction, guiding the design and execution of subsequent construction projects.

Three-dimensional numerical simulation
Model description. Basic assumptions. Many factors affect surface settlement during the shield tunnel construction. It is not possible to consider all factors during the simulation because of model complexity, long calculation time, and potential errors. The following assumptions were made to simplify the calculation while achieving accurate results.
The layers are distributed horizontally, the average thickness of the stratum is used, and the Mohr-Coulomb model is used to model the material response 24 .The Mohr-Coulomb model is selected because its parameters are easy to obtain, and it is suitable for engineering applications. It can accurately simulate the stress-strain relationship of the strata. Its disadvantage is that it assumes elastoplastic deformation of the strata. The Mohr-Coulomb criterion is used to predict formation failure. An elastic model that does not consider material nonlinearity for structural materials such as segments and shield shells is chosen because the material has a large stiffness, and only elastic deformation occurs during construction. The groundwater level remains unchanged during the construction, and consolidation settlement caused by a change in the groundwater level due to construction is ignored. The tunneling pressure, jack reaction force, and grouting pressure during the shield construction process  www.nature.com/scientificreports/ are simplified to apply uniform loads, and the average values of these parameters during the construction are used. The pressure on the excavation face, the jack's thrust force on the segment, the cutter head torque, and the total thrust force during the excavation of the shield tunneling machine are the same in the simulation as in the actual conditions. The shield grouting is simulated by adjusting the grouting pressure and the material properties of the grouting layer. The loading mode is shown in Fig. 6.
Boundary conditions and three-dimensional model. The shield tunnel construction was based on regional experience and on-site monitoring data. The impact range of shield construction is typically within 3 to 5 times the width of the tunnel, and the effect on the strata beyond this area is negligible. The tunnel in this case was a double-line circular tunnel with a single tunnel diameter of 6 m. The distance between the center lines of the two tunnels was 14 m, and the tunnel was buried at a depth of 19 m. The excavation was performed until reaching the 50th ring, which was an excavation length of 60 m. We considered the maximum value of the impact range in this simulation. The boundary of the model to the outside of the tunnel was 30 m. The simulation area for the first model establishment was 80 m × 60 m × 50 m. Displacement constraints were used at the boundary of the model, i.e., constraints in the X-and Y-directions were imposed on the side of the model to limit its horizontal movement. We applied constraints in the X-, Y-, and Z-directions at the bottom of the model. The top of the model represents the surface, and no constraints were imposed on the free surface. An initial stress field caused by the gravity load was applied to the model. The boundary conditions of the subsequent model were appropriately adjusted according to this principle. The three-dimensional model is shown in Fig. 7.  Tables 1 and 2.
Numerical simulation. In the actual shield construction project, the left tunnel was excavated first. The right tunnel was excavated after the 100th ring was completed on the left line (120 m of excavation). Asynchronous excavation was used until the tunnel was completed. Researchers have typically simplified the construction process by assuming the following three working conditions. In working condition 1, the excavation is completed on one side of the tunnel, and the excavation of the other side begins. Working condition 2 refers to the simultaneous excavation of the two tunnels in the same direction. Working condition 3 refers to excavating the left tunnel to a certain distance, followed by excavating the right tunnel (we call this asynchronous excavation). The sequence of shield construction in the three working conditions is shown in Fig. 8. It is observed in Figs. 11 and 12 that the simulated and measured surface settlement values in the initial excavation section (the first 100 rings) for working condition 1 are similar, and the curves exhibit the same trend. After the completion of the single-line excavation of the left tunnel, the measured maximum surface settlement is 13.8 mm. This measurement point is located above the central axis of the tunnel. The curves in Figs. 9 and 10 are V-shaped. The maximum settlement value obtained from the simulation is 18.2 mm. After the excavation of the right line is completed, the measured maximum surface settlement is 19.1 mm. This measurement point is located above the midpoint of the line connecting the central axis of the left and right tunnels. The settlement value of the original monitoring point has increased after the excavation, and the closer the point is to the center of the right tunnel, the larger the value is. The maximum settlement value in the simulation was 22.8 mm.
Working condition 2: In numerical simulations, the simultaneous construction of both tunnels is the simplest and fastest strategy; thus, this modeling method is widely used. However, it does not consider the influence of the construction process on the surface settlement. This method is not used in the actual project but is used in  www.nature.com/scientificreports/   Figure 15 shows the simulated and measured surface settlement after the completion of the double-line excavation for the three working conditions at y = 50 m. Figures 13,14,15 show that the simulated values of the surface settlement are consistent with the measured values for the three working conditions. The maximum surface settlement values obtained from the simulation are −23.2 mm, −23.6 mm, and −23.8 mm for the three working conditions, respectively. The values are similar for the three conditions. However, the measured settlement is 19.1 mm smaller than the simulated settlement. The measured and simulated surface settlement curves exhibit the same trend and have a V shape.
The models of working conditions 1 and 3 simulated the excavation of the tunnel in different stages of the project. The model of working condition 1 can also be used to simulate the excavation and construction of the other  www.nature.com/scientificreports/ side after the first tunnel has been completed. During the construction of a double-line tunnel, it is necessary to consider construction risks and costs related to uncontrollable factors, such as increased ground disturbance caused by the simultaneous construction of the left and right lines, the mechanical stability of the shield machine, and the difference in the technical expertise of the construction team. Although the simultaneous excavation of the two tunnels in the same direction (working condition 2) is not used in actual engineering, the modeling mode can be used to study the influence of the stratum parameters and other factors on the surface settlement. Working condition 2 is easier to implement than working condition 1 and working condition 3. Condition 2 is widely used in numerical simulations that do not consider asynchronous excavation and construction. The simulation of working condition 1 is the most consistent with the shield excavation 120 m before the tunnel in this engineering example. Moreover, the comparative analysis shows that the construction sequence in the numerical simulation has no significant influence on the surface settlement. In working condition 1, we simulated the single-line excavation first, followed by the double-line excavation to compare the results. Therefore, we use the model of working condition 1 in the subsequent analysis. The curve of the simulated settlement is smoother than that of the measured settlement. The analysis shows that the numerical simulation result is the ideal value under the assumed conditions. However, the factors affecting the surface settlement are complex in the real project. Mudstone is characterized by uneven weathering, and there are differences in the mechanical parameters of the rock and soil. The different layers are assumed to be continuous and have a uniform medium. The adjustment of the dynamic parameters during construction and the operation of heavy vehicles affect the monitoring results of surface subsidence.

Sensitivity analysis of surface subsidence parameters
Sensitivity of formation parameters. In this case study, shield construction is conducted in a strongly weathered mudstone layer. Weathered mudstone softens rapidly when it contacts water and easily disintegrates when it loses water. This stratum type typically exhibits uneven weathering. Differences in the physical and mechanical properties affect the surface settlement during shield construction. We analyzed the effects of the deformation modulus, cohesion, and internal friction angle of the strongly weathered mudstone layer on the surface settlement in working condition 1.  Fig. 18.
As the deformation modulus of the strongly weathered mudstone layer increases, the surface settlement decreases during single-line and double-line excavation. A significant decrease in the surface settlement is observed as the deformation modulus increases from 10 to 30 MPa. For example, the maximum surface  www.nature.com/scientificreports/ settlement during double-line excavation decreases from −57.9 to −23.2 mm, a decrease of 34.7 mm. As the deformation modulus increases, its influence on the surface settlement weakens. As the deformation modulus increases from 30 to 60 MPa, the maximum surface settlement during double-track excavation decreases from −23.2 to −11.8 mm, a decrease of 11.4 mm. These results indicate the significant influence of the deformation modulus on surface subsidence. Therefore, the uneven weathering of the mudstone layers in the formation should be considered.       www.nature.com/scientificreports/ The maximum surface settlement decreases with an increase in the distance between the two tunnels. At a distance of 11 m, the maximum surface settlement is −26.3 mm at the center between the two tunnels. As the distance increases to 23 m, the maximum surface settlement decreases to −20.4 mm. As the distance between the two tunnels increases, the width of the settlement trough increases, and the settlement curve changes from a V shape with an approximately normal distribution to a W shape with two peaks. The change in the shape of the surface settlement curve indicates that the mutual influence between the two tunnels decreases as the distance between the tunnels increases. In this working condition, the distance exceeds 20 m (> 3 D, where D is the diameter of the tunnel). The larger the spacing, the more pronounced the bimodal shape of the curve is.
Tunneling parameters of shield construction. The influence of the shield machine's thrust on surface settlement. The actual thrust of the shield machine is 9000-13000 kN. The thrust was simplified in the numerical simulation as a uniformly distributed load on the excavation surface of 300-430 kPa. Thrust values of 170 kPa, 300 kPa, 430 kPa, 560 kPa, and 690 kPa were used in the simulation, and the other parameters remained unchanged. The surface settlement for different thrust forces of the shield machine is shown in Fig. 28. The maximum surface subsidence occurred at monitoring point A (40, 30, 0).
The surface settlement values at monitoring point A (40, 30, 0) for different thrusts are shown in Fig. 29.  www.nature.com/scientificreports/ Figure 28 indicates that the surface settlement decreases as the thrust of the shield machine increases from 170 to 560 kPa. The maximum surface settlement decreases from 17.4 to 5.2 mm during single-line excavation and from 28.4 mm to 13.1 during double-line excavation. When the shield tunneling pressure is 690 kPa, there is no need to maintain the balance between the earth pressure of the shield machine and the earth pressure of the excavation face. The soil exhibits large deformation. The ground surface in front of the shield machine rises locally. After the shield machine passes, the ground surface begins to settle and stabilizes. The double-line tunnel shield machine results in a significant ground disturbance. Therefore, a significant change in the surface settlement is observed at a thrust of 690 kPa, and the effect is more pronounced for the double-line excavation. Figure 29 shows that a high thrust causes surface uplift in the initial stage of the left-line excavation, which is consistent with the actual results. After the excavation of the right line has started, a high thrust accelerates the increase in surface settlement. Thus, a suitable thrust should be chosen to reduce surface settlement. During the construction of the double-line tunnel, the shield machine significantly disturbs the stratum, especially in the middle of the left and right tunnels. Therefore, excessive thrust results in surface uplift and may cause greater surface settlement during double-line construction.
The influence of the shield grouting quality on surface settlement. Many factors affect the grouting quality, such as the ratio of the grouting liquid, the grouting pressure, and the grouting duration time. In this numerical simulation, the deformation modulus of the grouting layer is used as a proxy of the grouting quality. The deformation modulus of the grouting layer was E = 0.17 MPa, 1.7 MPa, and 17 MPa in the numerical simulation. The settlement values at the monitoring point of the profile at y = 50 m are shown in Fig. 30 and Fig. 31.  The influence of the section spacing between the left and right lines during asynchronous excavation on surface settlement. The model of working condition 3 was used to simulate the influence of the section spacing between the left and right lines (12 m (2D) and 24 m (4D), where D is the diameter of the tunnel) during asynchronous excavation on surface settlement. In working condition 1, the left line excavation was completed before the right line excavation was started, which was equivalent to a section spacing of d = 60 m. The distance was d = 0 m in the simultaneous excavation of the left and right lines (working condition 2). The surface settlement for different distances section spacings between the left and right lines is shown in Fig. 32.
The trends of the lateral surface settlement are similar for different section spacings during asynchronous excavation, and the curves show an approximately normal distribution. The maximum surface settlement is the largest (24.2 mm) at a section spacing of d = 12 m and the smallest (23.2 mm) at d = 60 m. A section distance of d = 0 m has the largest impact on the surface settlement (23.6 mm). However, the differences between the     www.nature.com/scientificreports/ maximum surface settlement values are very small for different section spacings, indicating that the section spacing is not a highly influential factor on the surface settlement during asynchronous excavation of doubleline shield construction.

Conclusion
We conducted finite element numerical simulations of a double-line tunnel construction project in the soft mudstone area of Changchun City and obtained field monitoring data to investigate the influence of various factors on the surface settlement. The following conclusions were drawn: 1. The numerical simulation results of the surface settlement during shield construction were consistent with the monitoring results, indicating the reliability of the numerical simulation method. The surface settlement curves of single-line and double-line shield construction had a "V" shape. 2. The surface settlement during shield construction is affected by many factors. The deformation modulus of the stratum had the largest influence on the surface settlement, and the tunnel's burial depth affected the surface settlement and its rate of change. Increasing the tunnel's burial depth can reduce the surface settlement in unfavorable stratum conditions.  www.nature.com/scientificreports/ 3. The thrust force during shield tunneling should be maintained within an appropriate range. Increasing the shield thrust within the critical range can reduce surface settlement, but the surface uplift in front of the shield tunneling machine occurs when the critical value is exceeded. The higher the grouting quality, the larger the deformation modulus of the grouting layer and the lower the surface settlement. The proposed numerical simulation method is suitable for optimizing the shield construction parameters. 4. The numerical simulation results showed that a change in the cross-sectional spacing between the left and right lines did not significantly influence the surface settlement. More monitoring data on dual-line asynchronous shield construction should be collected to obtain further insights into the influence of cross-sectional spacing during excavation.

Data availability
The data that supports the findings of this study are available in the supplementary material of this article. They are true and available, and are authorized by all the authors (Supplementary material).